17 - 1 CHAPTER 17 Capital Structure Decisions: Extensions  MM and Miller models  Hamada’s equation  Financial distress and agency costs  Trade-off models  Asymmetric information theory 17 - 2 Who are Modigliani and Miller (MM)?  They published theoretical papers that changed the way people thought about financial leverage.  They won Nobel prizes in economics because of their work.  MM’s papers were published in 1958 and 1963. Miller had a separate paper in 1977. The papers differed in their assumptions about taxes. 17 - 3 What assumptions underlie the MM and Miller models?  Firms can be grouped into homogeneous classes based on business risk.  Investors have identical expectations about firms’ future earnings.  There are no transactions costs. (More ) 17 - 4  All debt is riskless, and both individuals and corporations can borrow unlimited amounts of money at the risk-free rate.  All cash flows are perpetuities. This implies perpetual debt is issued, firms have zero growth, and expected EBIT is constant over time. (More ) 17 - 5  MM’s first paper (1958) assumed zero taxes. Later papers added taxes.  No agency or financial distress costs.  These assumptions were necessary for MM to prove their propositions on the basis of investor arbitrage. 17 - 6 Proposition I: V L = V U . Proposition II: r sL = r sU + (r sU - r d )(D/S). MM with Zero Taxes (1958) 17 - 7 Firms U and L are in same risk class. EBIT U,L = $500,000. Firm U has no debt; r sU = 14%. Firm L has $1,000,000 debt at r d = 8%. The basic MM assumptions hold. There are no corporate or personal taxes. Given the following data, find V, S, r s , and WACC for Firms U and L. 17 - 8 1. Find V U and V L . V U = = = $3,571,429. V L = V U = $3,571,429. EBIT r sU $500,000 0.14 17 - 9 V L = D + S = $3,571,429 $3,571,429 = $1,000,000 + S S = $2,571,429. 2. Find the market value of Firm L’s debt and equity. 17 - 10 3. Find r sL . r sL = r sU + (r sU - r d )(D/S) = 14.0% + (14.0% - 8.0%)( ) = 14.0% + 2.33% = 16.33%. $1,000,000 $2,571,429 [...].. .17 - 11 4 Proposition I implies WACC = rsU Verify for L using WACC formula WACC = wdrd + wcers = (D/V)rd + (S/V)rs $1,000,000 = $3,571,429 (8.0%) ( ) $2,571,429 +($3,571,429)(16.33%) = 2.24% + 11.76% = 14.00% 17 - 12 Graph the MM relationships between capital costs and leverage as measured by D/V Without taxes Cost of Capital (%) 26 rs 20 WACC 14 rd 8 0 20 40 60 80 Debt/Value 100 Ratio (%) 17 -... ) 17 - 28 2 However, personal tax laws favor equity over debt because stocks provide both tax deferral and a lower capital gains tax rate 3 This lowers the relative cost of equity vis-a-vis MM’s no-personaltax world and decreases the spread between debt and equity costs 4 Thus, some of the advantage of debt financing is lost, so debt financing is less valuable to firms 17 - 29 What does capital structure. .. for corporate managers? 1 MM, No Taxes: Capital structure is irrelevant no impact on value or WACC 2 MM, Corporate Taxes: Value increases, so firms should use (almost) 100% debt financing 3 Miller, Personal Taxes: Value increases, but less than under MM, so again firms should use (almost) 100% debt financing 17 - 30 Do firms follow the recommendations of capital structure theory? 1 Firms don’t follow... $1,542,857 = 14.0% + 2.33% = 16.33% 17 - 20 4 Find Firm L’s WACC WACCL = (D/V)rd(1 - T) + (S/V)rs $1,000,000 = $2,542,857 (8.0%)(0.6) $1,542,857 + $2,542,857 (16.33%) ( ( ) ) = 1.89% + 9.91% = 11.80% When corporate taxes are considered, the WACC is lower for L than for U 17 - 21 MM relationship between capital costs and leverage when corporate taxes are considered Cost of Capital (%) rs 26 20 14 8 0 20... is unaffected by leverage 17 - 15 Find V, S, rs, and WACC for Firms U and L assuming a 40% corporate tax rate With corporate taxes added, the MM propositions become: Proposition I: VL = VU + TD Proposition II: rsL = rsU + (rsU - rd)(1 - T)(D/S) 17 - 16 Notes About the New Propositions 1 When corporate taxes are added, VL ≠ VU VL increases as debt is added to the capital structure, and the greater... corporate taxes are considered 17 - 17 1 Find VU and VL EBIT(1 - T) = $500,000(0.6) = $2,142,857 VU = 0.14 rsU Note: Represents a 40% decline from the no taxes situation VL = VU + TD = $2,142,857 + 0.4($1,000,000) = $2,142,857 + $400,000 = $2,542,857 17 - 18 2 Find market value of Firm L’s debt and equity VL = D + S = $2,542,857 $2,542,857 = $1,000,000 + S S = $1,542,857 17 - 19 3 Find rsL rsL = rsU... rsU, then larger values of the tax shield don't change the risk of the equity 17 - 35 Levered beta If there is growth and rTS = rsU then the equation that is equivalent to the Hamada equation is β L = β U + (β U - β D)(D/S) Notice: This looks like Hamada without taxes Again, this is because in this case the tax shield doesn't change the risk of the equity 17 - 36 Relevant information for valuation ... WACC 14 rd 8 0 20 40 60 80 Debt/Value 100 Ratio (%) 17 - 13  The more debt the firm adds to its capital structure, the riskier the equity becomes and thus the higher its cost  Although rd remains constant, rs increases with leverage The increase in rs is exactly sufficient to keep the WACC constant 17 - 14 Graph value versus leverage Value of Firm, V (%) VU 4 VL 3 Firm value ($3.6 million) 2 1 0... corporate tax rate Td = personal tax rate on debt income Ts = personal tax rate on stock income [ ] 17 - 24 Tc = 40%, Td = 30%, and Ts = 12% [ ] VL = VU + 1 - (1 - 0.40)(1 - 0.12) D (1 - 0.30) = VU + (1 - 0.75)D = VU + 0.25D Value rises with debt; each $100 increase in debt raises L’s value by $25 17 - 25 How does this gain compare to the gain in the MM model with corporate taxes? If only corporate... think debt ratios were too low, and MM led to changes in financial policies 17 - 31 How is all of this analysis different if firms U and L are growing?  Under MM (with taxes and no growth) VL = VU + TD This assumes the tax shield is discounted at the cost of debt  Assume the growth rate is 7%  The debt tax shield will be larger if the firms grow: 17 - 32 7% growth, TS discount rate of rTS Value . 17 - 1 CHAPTER 17 Capital Structure Decisions: Extensions  MM and Miller models  Hamada’s equation  Financial distress. 14.00%. $1,000,000 $3,571,429 $2,571,429 $3,571,429 17 - 12 Graph the MM relationships between capital costs and leverage as measured by D/V. Without taxes Cost of Capital (%) 26 20 14 8 0 20 40 60 80. (%) 26 20 14 8 0 20 40 60 80 100 Debt/Value Ratio (%) r s WACC r d 17 - 13  The more debt the firm adds to its capital structure, the riskier the equity becomes and thus the higher its cost.  Although